A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?

Correct answer:

S =  115.6965 m2

Step-by-step explanation:

D=6 m R=D/2=6/2=3 m  sinα=r/s  R:(hR)=r:s=sinα  r=s hRR  S=π r s=π R/(hR) s2  S=π R/(hR) ((R/(hR))2+h2)  S=(3(9/(3+h)2+h2)π)/(3+h)  h=6.372526.3725 m  s=(R/(hR))2+h2=(3/(6.37253))2+6.372526.4343 m r=s hRR=6.4343 6.3725335.7236 m  S=π r s=3.1416 5.7236 6.4343=115.6965 m2

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